An explicit solvent model of coacervate structure and thermodynamics

Complex coacervation, a liquid-liquid phase separation phenomenon driven by electrostatic interactions between oppositely charged polyelectrolytes (PEs), has attracted widespread attention because of its relevance in biological systems and potential applications in materials science. Although many theoretical models, experimental investigations, and computational studies have investigated the thermodynamics, phase coexistence behavior, and rheological properties in great detail, a molecular-level understanding of the internal structure of the complex coacervate phase is still lacking. In this study, we investigate the effects of degree of polymerization of the polyelectrolytes ($N$) on the phase behavior and internal structure of the resulting coacervate phase using molecular dynamics simulations employing a simplistic bead-spring model of polyelectrolytes and explicit nonpolar solvents. Our simulations show an increase in coacervate phase stability with $N$, elevating the critical temperature in agreement with existing theoretical predictions and experimental observations. The polyelectrolytes inside the dense phase maintain a homogeneous overlapping distribution without collapsing into globules. The compactness of the dense phase increases with $N$ agreeing prior experimental observations, despite a concomitant increase in the polymer's effective size as quantified by its radius of gyration ($R_{ m g}$). We discuss the implications of this model for fundamental understanding of the coacervation process, and as first step toward systematic examination of the mutual role of electrostatics and chemistry in the behavior of solvated polyions.